new robert b. sosman - nistfuller/presentations/sosman... · 2004. 5. 4. · preservation of...

Ceramics Division

Robert B. Sosman

B.Sc., Ohio State University, 1903Ph.D., M.I.T., 1907 (1st yr.; 1 of 3)Arthur D. Little, 1906-1908Geophysical Laboratory, 1908-1928U.S. Steel Corp., 1928-1947Rutgers University, 1947-1962The Properties of Silica, 1927; The Phases of Silica, 1965Hiker, 7th to complete Appalachian Trail (Maine-Georgia)Dancer & Dining, Gustavademecum for the Island of Manhattan

Physical ChemistPresident, The American

Ceramic Society, 1937–38Edward Orton Jr. Lecturer, 1937Albert V. Bleininger Award, 1953Ross C. Purdy Award, 1957John Jeppson Medal, 1960

James B. Austin, Proc. Geological Society of America, 251-258 (1968).

1881-1967

Edwin R. Fuller, Jr.National Institute of Standards and Technology

Gaithersburg, MD 20899-8522, U.S.A.

<[email protected]>

Microstructural Stresses:Networks, Structural Reliability,

& Antiquity Preservation

Robert B. Sosman Memorial Lecture106th Annual Meeting of

The American Ceramic SocietyIndianapolis, IN - April 21, 2004

Ceramics Division

Predict Reliability ofCeramic-Containing Components

Kovar contactKovar washer

Alumina

Kovar sleeve

Header

Ag braze

residual stresses can cause spontaneous microcracking and influence R-curve behavior & crack propagation under applied loads

Venkata R. Vedula, Shekhar Kamat & S. Jill Glass, Sandia National Laboratories

thermal expansionmismatch

thermal expansion anisotropy

Residual Stresses due to:

-

+

0

-

+

0

Ceramics Division

Thermal Degradation of Decorative Marbles

Thomas Weiß and Siegfried Siegesmund, Universität Göttingen, Germany

bowing of façade claddings (library,

Universität Göttingen)

granulardisintegrationoriginal

after 6 years

Ceramics Division

Preservation of Antiquity ArtifactsJewish cemetery in Hamburg Altona (marble tombstones)

Siegfried Siegesmund, Thomas Weiß & Joerg Ruedrich, Universität Göttingen, Germany

Harp Player (marble)Early Cycladic

2700-2300 B.C.Getty Conservation Institute

museum, Los Angeles

Ceramics Division

Microstructural Stresses

to elucidate the influence of various types of texture on microstructural residual stresses and related ensemble physical behavior and properties of polycrystalline ceramics

Objective:

Contents:Residual-Stress Networks

in Polycrystalline CeramicsMicrostructural Finite-Element AnalysisStatistical Description

of Microstructure and TextureResidual Stress and

Physical Property SimulationsThe Old and the New

Ceramics Division

Origin ofMicrostructural Stresses

Internal microstructural stresses arise due to Thermal Expansion Anisotropy (TEA) misfit between adjacent grains uponheating or cooling

-6 ppm/K

26 ppm/K

-6 ppm/K

calcite

Ceramics Division

Thermal Expansion AnisotropyMisfit Strains in a Microstructure

Cooling from strain-free temperature

Ceramics Division

Thermal Expansion AnisotropyMisfit Strains in a Microstructure

¤ Microstresses are independent of grain size ¤

Cooling from strain-free temperature

<G> = 36 µm

100 µm

Grain Orientations from EBSDelectron beam

Ceramics Division

Kikuchi bands

Electron Back-

Scattered Diffraction

500 µm

Grain Orientations from EBSDelectron beam

Ceramics Division

Kikuchi bandsalumina

Electron Back-

Scattered Diffraction

measure with piezo-or micro-Raman spectroscopy

Ceramics Division

Calculation of Microstructural Residual Stresses

Microstructure

Thermoelastic PropertiesC11, C12, C13, C33, C14, C44α11, α33

microstructural finite element

analysisGrain Orientations

EBSP

EBSD

Microstructural Residual Stresses

Ceramics Division

Stress Networks in Alumina

V.R. Vedula, S.J. Glass, D.M. Saylor, G.S. Rohrer, W.C. Carter, S.A. Langer, and E.R. Fuller, Jr., J. Am. Ceram. Soc., 84 [12], 2947-2954 (2001).

untextured EBSDmicrostructure

Grain Normals

Residual Stress Distribution upon cooling by 1500°C

Max. PrincipalStress (MPa)

Ceramics Division

Residual Stress Distribution in Untextured Alumina (∆T = -1500°C)

EBSDmicrostructure

HydrostaticStress (MPa)

Max. PrincipalStress (MPa)

Contents:

Ceramics Division






Microstructural Finite-Element Analysis

Ceramics Division

5 µm

NiO

ZrO2

Fe2TiO5

10 µm

Bimodal Si3N4

Material Microstructures: Heterogeneous & Stochastic

Air-Plasma-SprayedThermal Barrier Coating

Ceramics Division

Public domain software to simulate and elucidate macroscopic properties of complex materials microstructures

http://www.ctcms.nist.gov/oof

Object Oriented FiniteElement Analysis

for Materials Science and Engineering

1999 Technologies of the Year Award

Ceramics Division

Building a Microstructural ModelSimulationsExperiments

Visualization of Microstructural Physics

Virtual ParametricExperiments

Effective MacroscopicPhysical Properties

FundamentalMaterials Data

MaterialsPhysics

Microstructure Data(micrographs)

easy-to-use Graphical User Interface (GUI) – ppm2oof

Object StructureIsomorphic to the Material

Finite Element Solver

easy-to-use Graphical User Interface (GUI) – oof

Ceramics Division

Finite Element Analysis of Real Microstructuresa tool for materials scientists

to design and analyze advanced materials

ppm2oof: a tool to convert a micrograph or image of a complex, heterogeneous microstructure into a finite element mesh with constitutive properties specified by the user.

Point, Click,and SpecifyProperties

Real ( orSimulated)

Microstructure

oof: a tool to perform virtual experi-ments via finite element analysis to elucidate microstructural properties and macroscopic behavior.

Visualize andQuantifyVirtual Test

δT

oof2abaqus: converts PPM2OOF or OOF data files into input files for ABAQUS™.

Ceramics Division

Convert micrograph to “.ppm” (portable pixel map) fileSelect & identify phases to create segmented imageAssign constitutive physical properties to each phaseMesh in PPM2OOF via “Simple Mesh” or “Adaptive Mesh” – multiple algorithms that allow elements to adapt to the microstructure

PPM2OOF Tool

Segmented Image Mesh

Micrograph

Ceramics Division

Adaptive Meshing by Components

pixel imagewith mesh

mesh

pixelimage

Generate a finite-element meshfollowing the material boundaries

Ceramics Division

Eshape = 0

Eshape → 1

Ehom. > 0

Ehom. = 0

Adaptive Meshing by Components: refine elements and move nodes via Monte Carlo

annealing to reduce E = (1-α)Eshape + αEhomogeneity

createmesh

swap worstto reduce E

anneal toreduce Eimage

Ceramics Division

OOF Tool

Perform virtual experiments on finite-element mesh:To determine effective macroscopic propertiesTo elucidate parametric influencesTo visualize microstructural physics

Visualize & Quantify:Heat Flux Distribution

Virtual Experiments:Temperature Gradient

To - δT

To + δT

OOF 2.0 Current Development EffortStephen A. Langer, Andrew C. E. ReidSeung-Ill Haan, and Edwin Garcia

Ceramics Division

• Ψ = fEquil. Eq.:Ψ = Σ c • φConstitutive Eq.:

Extensible and more flexible platformEnhanced image analysis toolsExpanded element typesGeneralized constitutive relations (elasticity, piezoelectricity, etc.) w/coupling between fields

Linear and nonlinear solvers with automatic mesh refinement

– ppm2oof and oof are now combinedPlanned Additions

3-dimensional finite element solverTime-dependent solver Plasticity

Ceramics Division

Development TeamOOF

Edwin Garcia

Andrew Reid

Steve Langer Seung-Ill Haan

Craig Carter

Contents:

Ceramics Division






Statistical Descriptionof Microstructure and Texture

Ceramics Division

Statistical Descriptionof Microstructure

Microstructure Descriptor: h = {c, φ, g, …}• composition: c• phase: φ• crystal orientation: g = {ϕ1, Φ, ϕ2}

Microstructure Statistics• 1-point statistics: f1(h)• 2-point statistics: f2(h, h’ | r )

Grain-Boundary Statistics: S(∆g, n)

rg

sampleaxes

crystalaxes

adapted fromSurya R Kalidindi

Ceramics Division

Types of TextureCrystallographic Textureo Orientation Distributions Functions (ODF) of

grains: g = {ϕ1, Φ, ϕ2}• Random in Euler Space (uniform)

• March-Dollase Fiber Texture

• Others ODF’so Intercrystalline Misorientation Distributions

Functions (MDF): uniform and high & lowo Orientation Correlation Functions (k-point

statistics)Grain-Shape Morphologic Texture

ϕ1 ∈ {0, 2π}cos[Φ] ∈ {-1, 1}

ϕ2 ∈ {0, 2π}

f(M,θ) = M/[cos2(θ) + M sin2(θ)]3/2

M: max. MRD

θ

Ceramics Division

UniformCrystallographic Texture

15105

45

13575

165

ODF

0 30 60 90 120 150 180

uniform

Ceramics Division

Types of Misorientation Texture

0 30 60 90

low

15

105

45

135

75

1653060 90 30 60 90

0 30 60 90

uniform

0 30 60 90

high

MDF

∆θ:

15

105

45

135

75

16590 60 90 60 90 30∆θ:

15

105

45

135

75

1653030 60 30 60 90∆θ:

Contents:

Ceramics Division






Residual Stress and Physical Property Simulations

Ceramics Division

Simulation Model Microstructure

3-D:422 grains1003 voxels

2-D:924 grains

10002 pixels

Grains:same composition: either calcite, dolomite, or aluminasame thermoelastic properties

Orientations:different crystallographic orientations for all grainsrandom or c-axis textured distribution of crystalline orientationsuniform, and high and low distribution of intergranular misorientations

Ceramics Division

Microstructure Crystallography

Intergranular Misorientation Distributions:

Crystalline Orientations Distributions:

freq

.

0.0

0.1

0.2

0.3

0 15 30 45 60 75 90θ(°)

“low”

freq

.

0.3

0.0

0.1

0.2

0 15 30 45 60 75 90θ(°)

“uniform”

freq

.0.0

0.1

0.2

0.3

0 15 30 45 60 75 90θ(°)

“high”

Max MRD = 8

8.0

0.0

4.0

MRDMax MRD = 20

20

0

10

MRDMax MRD = 1

1.1

0.9

1.0

MRD

Ceramics Division

Phenomena Influencedby Texture

Microstructural Residual StressesElastic Strain Energy Density (a measure of microcracking propensity)Anisotropy in Bulk Thermal Expansion CoefficientAnisotropy in Bulk

Elastic ModulusMicrocracking and

its influence on properties

0 200 400 600 800 1000 1200 1400

Temperature / °C

260

280

300

320

340

360

380

400

Youn

g's M

odul

us /

GPa

heating

cooling: heating: cooling

S. Galal Yousef & J. RödelT U Darmstadt

Ceramics Division

Influence of Grain Misorientation

Distribution Functionfor a random grain orientation

distribution function

on residual stresses in polycrystalline calcite upon

heating by 100 ºC

maximum principal stress for a random grain orientation distribution function

Ceramics Division

random grain orientation distribution function

Influence of Grain Misorientation

Distribution Function

low-angle GB’suniform

high-angle GB’s

400 MPa0

35.3 ± 1.0 kJ/m3

32.3 ± 1.9 kJ/m3

23.7 ± 2.4 kJ/m3

Ceramics Division

Calcite Results

Maximum Principal Stress upon heating +100ºC for 5 random orientation distributions of calcite grains

MDF

Low

Unifo

rm#1 #2 #3 #4 #5

High

ODF:5 replications

Ceramics Division

Alum

ina Results

Maximum Principal Stress upon cooling 1500ºC for 5 random ODF‘s orientation distributions of alumina grains

MDF

Unifo

rmLo

wHigh

#1 #2 #3 #4 #5ODF:5 replications

Ceramics Division

Elastic Strain Energy Density

K (GPa)

∆α • ∆T (ppm)∆α = α3 − α1

<Elast

ic E

nerg

y Den

sity

> (k

J/m

3 ) 5 replications ODF:random(MRD=1)

MDF:o higho uniformo low

76

32 • 100

99

20 • 100

251

0.75 • 1500

Ceramics Division

Normalized Elastic Energy DensityN

orm

aliz

ed <E

last

ic E

nerg

y D

ensi

ty>

W/K

•(∆

α•∆

T)2

K (GPa)76 99 251∆α • ∆T (ppm)32 • 100 20 • 100 0.75 • 1500

ODF:random(MRD=1)


Ceramics Division

Types of Thermal Expansion

Carrara (Italy)Carrara (Italy) Kauffung (Poland)Kauffung (Poland)Carrara (Italy)Carrara (Italy)

Ceramics Division

<CTE

> (1

0-6 /

K)Bulk Coefficient of Thermal Expansion

4.67

12.67

8.87

<α> = (2α1+α3)/3

αx αy αx αy αx αy

5 replications ODF:random(MRD=1)

MDF:o higho uniformo lowy

x

Ceramics Division

Normalized Bulk CTECT

E /<

α>

<α> = (2α1+α3)/3MRD = 1MDF:o higho uniformo low

αx αy αx αy αx αy

y

x

Ceramics Division

Venkata R. Vedula, Edwin R. Fuller, Jr. , and S. Jill Glass

Hydrostatic Stress, (σ11 + σ22), for ∆T = -1500 °C

Residual Stresses in Aluminawith Crystallographic Textured

+567

+300

+ 33

-234

-501

-767

Untextured (MRD=2)

+532

+299

+ 66

-167

-401

-635

Textured (MRD=90)


Ceramics Division

Elastic Strain Energy Densityfor textured calcite heated +100°C

<Elast

ic E

nerg

y Den

sity

> (k

J/m

3 )

ODF: MRD

texture c-axis along y-axis

texturedrandom

texturedrandom


<CTE

> (1

0-6 /

K)

ODF: MRD

αx

αy

αx

αy

αx

αy isotropic <α> = (2α1+α3)/3= 4.67

Ceramics Division

Bulk Thermal Expansion Anisotropyfor textured calcite heated +100°C


Ceramics Division

3-D Simulations: Elastic Energy Density

1

20

MDF“high” “low”

EED

(kJ/

m3 )

100

0

49 kJ/m3

41 kJ/m3

50 kJ/m3

18 kJ/m3

alumina cooled by 1000°C

ODF

(max

MRD

)

Ceramics Division

3-D Simulations: Elastic Energy Density

1

20

MDF“high” “low”

EED

(kJ/

m3 )

100

0 alumina cooled by 1000°C

ODF

(max

MRD

)

isosurfaces for energy density > 100 kJ/m3

Ceramics Division

Elastic Strain Energy Densityfor textured alumina cooled 1000°C

<Elast

ic E

nerg

y Den

sity

> (k

J/m

3 )


ODF: MRD

3 replications

texturedrandom


Ceramics Division

Bulk Thermal Expansion Anisotropyfor textured alumina cooled 1000°C


<CTE

> (1

0-6 /

K)

ODF: MRD

α⊥

αll

α⊥

αll

α⊥

αll

isotropic <α> = (2α1+α3)/3= 8.87

3 replications

texturedrandom


What is a good metric for characterizingresidual-stress isosurfaces?

Ceramics Division

Residual-Stress Isosurfaces

e.g., isosurface of elastic energy densities greater than 100 kJ/m3

homology groups and topological invariants — measure the topological complexity of objects in any dimension.

Thomas Wanner, George Mason University, proposed the use of:

Ceramics Division

Residual-Stress Isosurfaces

e.g., isosurface of elastic energy densities greater than 100 kJ/m3

Ceramics Division

Computational Algebraic Topology

CHomP (Computational Homology Program): pixel/voxel oriented public-domain software for computing algebraic topological invariants. Associated New Textbook: Computational Homology by Tomasz Kaczynski, Konstantin Mischaikow , and Marian Mrozek, (Applied Mathematical Sciences , Vol. 157, Springer-Verlag, 2004).

Challenge in Computational Algebraic Topology:Theoretically, determination of homology groups and topological invariants is straightforward.Computationally, such determination may be intractable or infeasible for large data sets.

Algebraic Topology:a branch of mathematics, in which tools from abstract algebra are used to study topological spaces.

Ceramics Division

Topological Invariants of Space

Topological Invariants of a Complex ObjectBetti numbers, named for Enrico Betti, are a sequence β0, β1, ... of topological invariants, which are natural numbers, or infinity.Other invariants include: torsion coefficientsand the Euler characteristic.

Homology groups: a more general measure of the complexity of the object in any dimension.

… invariant under transformations that do not require cutting or gluing of the object.

Ceramics Division

Zeroth Betti NumbersBetti number β0 counts the number of connected components of the structure

How many distinct connected regions does the maze have?

Computational Homology, Applied Mathematical Sciences , Vol. 157, Springer-Verlag, 2004).

Ceramics Division

Zeroth Betti NumbersBetti number β0 counts the number of connected components of the structure

Computational Homology, Applied Mathematical Sciences , Vol. 157, Springer-Verlag, 2004).

Cut along the blue lines: the zeroth Betti number is the number of pieces that the maze falls apart into.

Ceramics Division

First Betti NumberBetti number β1 counts the number of independent tunnels created by the structure: the number of loops in the structure that cannot be

shrunk to a point, ormorphed into each other.

β1 = 0 β1 = 2

β1 = 4

Ceramics Division

Second Betti NumberBetti number β2 counts the number of

closed regions created by the structure.

all surfaces have β2 = 1

Ceramics Division

Max. Principal Stress Networks

Thomas Wanner, George Mason UniversityKonstantin Mischaikow, Georgia Institute of Technology

isosurface forσ1 > 201 MPa

β2

β1

β0

Threshold Level for Max. Principal Stress

Bett

i num

ber

Ceramics Division

Max. Principal Stress Networks

Thomas Wanner, George Mason UniversityKonstantin Mischaikow, Georgia Institute of Technology

isosurface forσ1 < 27.5 MPa β2

β1

β0

Threshold Level for Max. Principal Stress

Bett

i num

ber

Contents:

Ceramics Division





Physical Property SimulationsMonument RestorationThe Old and the New

The Tomb of the Unknowns

Ceramics Division

Made from a 55-ton block of white marble from the Yule Marble Quarry located near Marble, Colorado, the monument was dedicated in 1932.

A crack, first discovered in the 1940’s during the Truman administration, has continued to grow.

Unknowns Monument Will Be ReplacedBy Annie Gowen, The Washington Post, Monday, May 26, 2003, B01

“The growing crack that now circles the marble monument has split the three figures representing Peace, Victory and Valor.”

(James A. Parcell - The Washington Post)

“Officials decided to replace the stone after concluding that a 1989 cosmetic repair job — which cemetery historian Thomas Sherlock compared to fixing a bathtub with tile grout — had done nothing to conceal the problem and may have exacerbated it.”

Ceramics Division

Microstresses are independent of grain size

Residual Stressesin Nanostructured Ceramics

Ceramics Division


Ceramics Division

new phenomena (physics) at the small-scale? e.g., surface stresses: σij = γ δij + (∂γ/∂εij)


Ceramics Division

100 µm

6 µm

new phenomena (physics) at the small-scale? e.g., surface stresses: σij = γ δij + (∂γ/∂εij)

Ceramics Division

Collaborators & AcknowledgmentsStephen A. Langer, Information Tech. Lab, NISTAndrew C. E. Reid, Edwin Garcia, & Seung-Ill Haan, MSEL, NISTW. Craig Carter, MITDavid M. Saylor, U.S. Food and Drug AdministrationEdward Lin, Montgomery Blair High SchoolThomas Weiß & Siegfried Siegesmund, Geowissenschaftliches Zentrum der Universität Göttingen, GermanyThomas Wanner, George Mason UniversityAndré Zimmermann, Bosch GmbH, GermanySusan Galal Yousef & Jürgen Rödel, Technische Universität Darmstadt, GermanyVenkata R. Vedula, Shekhar Kamat, Raj Tandon, Saundra Monroe, S. Jill Glass & Clay Newton, Sandia Natl. LabsChang-Soo Kim & Gregory S. Rohrer, Carnegie Mellon UniversityAlbert Paul and Grady White, MSEL, NISTBarbara Fuller

Ceramics Division

AbstractMicrostructural Stresses: Networks, Structural

Reliability, & Antiquity PreservationEdwin R. Fuller, Jr.

National Institute of Standards and Technology,Gaithersburg, Maryland 20899-8522, U.S.A.

Macroscopic behavior and ensemble physical properties of heterogeneous materials, such as polycrystalline ceramics or stone, depend on the thermoelastic properties of the constituent phases, their morphology, and their topology. Or simply, on the crystallites, their shape, and how they are arranged. Because crystalline properties are typically anisotropic, this dependence encompasses the distribution of crystallite orientations (crystallographic texture) as well as distributional aspects of crystallite shape and spatial arrangements. A property profoundly affected by these heterogeneous and stochastic features is the internal, or microstructural stresses. Their influence on behavior can be either deleterious, as in performance degradation of ceramic components or physical deterioration of stone sculptures and monuments, or advantageous, as in transformation and grain-bridging toughening phenomena. Microstructural stresses occur from many causes: temperature changes in conjunction with thermal expansion differences between features, phase transformations, or crystallization of fluids or salts in pores (e.g., freeze/thaw cycles). Many materials science tools are available to elucidate these phenomena. Computational materials science, however, provides a particularly facile means for examining material response to a wide variety of physical conditions. A recently observed phenomenon in polycrystalline materials with crystalline thermal expansion anisotropy is the development of residual-stress networks upon cooling or heating. Moreover, the length-scale of these networks encompasses many grains. To study this and related phenomena, two- and three-dimensional model microstructures were generated with a pixel/voxel-based tessellation technique that constructs grains whose morphologies conform to a predefined statistical distribution. Crystal orientations were overlaid on the grain structure such that grain orientation and misorientation distribution functions also match predefined statistical distributions. Microstructure-based finite-element simulations were then used to elucidate the origin of the residual stress networks, and to characterize the influence of texture on network size and associated polycrystalline physical properties, such as bulk thermal expansion and microcracking propensity.

new robert b. sosman - nistfuller/presentations/sosman... · 2004. 5. 4. · preservation of...

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